Problem: Multiply the following complex numbers: $({-2-3i}) \cdot ({-5-2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2-3i}) \cdot ({-5-2i}) = $ $ ({-2} \cdot {-5}) + ({-2} \cdot {-2}i) + ({-3}i \cdot {-5}) + ({-3}i \cdot {-2}i) $ Then simplify the terms: $ (10) + (4i) + (15i) + (6 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 10 + (4 + 15)i + 6i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 10 + (4 + 15)i - 6 $ The result is simplified: $ (10 - 6) + (19i) = 4+19i $